Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0003)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

Values at z=1

For fixed a₁, a₂, a₃, b₁, b₂

http://functions.wolfram.com/07.27.03.0003.01

Input Form

HypergeometricPFQ[{a, b, c}, {d, e}, 1] == Sqrt[Gamma[1 - a]] Sqrt[Gamma[1 - b]] Sqrt[Gamma[1 - c]] Gamma[d] Gamma[e] Sqrt[Gamma[d + e - a - b - c]] (ClebschGordan[{(d - a - b - 1)/2, (b + d - a - 1)/2}, {(e - a - c - 1)/2, (a + 1 - c - e)/2}, {(d + e - b - c)/2 - 1, (b + d - c - e)/2}]/(Sqrt[-1 - b - c + d + e] Sqrt[Gamma[-a + d]] Sqrt[Gamma[-b + d]] Sqrt[Gamma[-c + d]] Sqrt[Gamma[-a + e]] Sqrt[Gamma[-b + e]] Sqrt[Gamma[-c + e]])) /; Re[d + e - a - b - c] > 0

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]